Question
upstudy study bank question image url

1.3 If \( \left(A^{T}+1\right)^{-1}=\left[\begin{array}{cc}-1 & 2 \\ -3 & 7\end{array}\right] \) is singular if (a) The matrix is not invertable b) \( \left[\begin{array}{cc}-6 & 2 \\ -3 & 2\end{array}\right] \) c) \( \left[\begin{array}{cc}8 & -2 \\ 3 & 0\end{array}\right] \) d) \( \left[\begin{array}{cc}-6 & -3 \\ 2 & 2\end{array}\right] \) e) None of the above

Ask by Harris Ward. in Saudi Arabia
Mar 09,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

None of the provided matrices are singular.

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

Bonus Knowledge

To determine when the matrix \( \left(A^{T}+1\right)^{-1} \) is singular, we need to assess if its determinant is zero. A matrix is singular if it is not invertible, meaning its inverse does not exist. Now, let's analyze the offered matrices. The first matrix can be rewritten in terms of its determinant, which will help us identify singular cases. For options (b), (c), and (d), we can calculate the determinants easily: (b) For \( \left[\begin{array}{cc}-6 & 2 \\ -3 & 2\end{array}\right] \), the determinant is calculated as \((-6)(2) - (2)(-3) = -12 + 6 = -6\) (not singular!). (c) For \( \left[\begin{array}{cc}8 & -2 \\ 3 & 0\end{array}\right] \), the determinant calculates to \(8 \cdot 0 - (-2) \cdot 3 = 0 + 6 = 6\) (not singular). (d) For \( \left[\begin{array}{cc}-6 & -3 \\ 2 & 2\end{array}\right] \), the determinant is calculated as \((-6)(2) - (-3)(2)= -12 + 6 = -6\) (not singular). Thus, the correct answer is (e) None of the above, since all matrices listed do not make \( \left(A^{T}+1\right)^{-1} \) singular.

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy